Enhanced second-harmonic generation by double-resonant mode matching in deep-subwavelength nonlocal polar dielectric cylinder

Enhancing nonlinear light–matter interactions in deep-subwavelength nanostructures remains a central challenge in nonlinear nanophotonics. Second-harmonic generation (SHG) offers an important route for nonlinear frequency conversion, but its efficiency at the nanoscale is often limited by weak nonlinear interactions and the difficulty of simultaneously matching the fundamental and second-harmonic resonances. Here, we investigate enhanced SHG in a polar dielectric core–shell cylinder with spatial dispersion (nonlocal effect) through double-resonant mode matching in the deep-subwavelength range (radius ∼ λ0/1000). Pronounced SHG enhancement can be achieved when the resonances at the fundamental and second-harmonic frequencies are simultaneously satisfied. Compared with the local-response case, which supports only a single dominant resonance branch, the nonlocal response introduces additional longitudinal optical phonon modes and provides additional resonant channels for matching the fundamental and second-harmonic modes. Moreover, the nonlinear response is highly sensitive to the shell permittivity and the surrounding medium. These findings suggest a promising route for enhancing nonlinear frequency conversion and developing high-sensitivity mid-infrared nonlinear sensors based on nonlocal polar dielectric nanostructures.